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<div class="moz-cite-prefix">Dan,<br>
<br>
I assume you mean in-plane focusing, not vertical focusing which
would require out-of-plane field measurements. It will be
interesting to see what you find the sensitivity to be. The plan
you have to test it by interpolating the existing TOSCA map with
full and degraded resolution, and tracking electrons through it
sounds like it will tell us the sensitivity to the grid spacing at
the edge. Sounds good.<br>
<br>
-Richard J.<br>
<br>
<br>
On 7/18/2013 11:27 AM, Daniel Sober wrote:<br>
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<blockquote cite="mid:51E80947.3060505@cua.edu" type="cite">
Richard,<br>
The error in the field integral is hard to quantify -- it depends
on how the raytracing codes interpolate between the field points
(probably effectively linearly). In any case, the important
question is the effect on the position and direction of the
electrons at the focal plane. A substantial error in B at the
exit edge may influence the focusing without having much effect on
integral B*L. I am trying to refresh my knowledge of SNAKE (with
the help of John LeRose), and run some tagger orbits through the
Tosca field using several grids: 1x1 cm (as provided by Yang),
1x2 cm (close to what we expect to map) and 2x2 cm. If the 2x2
results are in acceptable agreement with the 1x1 (I would say
within +-1/2 microscope fiber is acceptable) then we don't need to
worry.<br>
<br>
Tim, <br>
As I look closer at my plots of fields at different magnet
excitations, I think we can live with a fairly sparse grid of
measurements at fields other than 15 kG, and then fit some kind of
smooth ratio function to the 15 kG map.<br>
<br>
How long do you anticipate a full 1x2.5 cm map will take, and how
much time would be saved by increasing the step size by factors of
2 or 4 in each direction? Do we plan to measure several field
values for each mapper setup before moving the apparatus?<br>
<br>
Dan<br>
<br>
<div class="moz-cite-prefix">On 7/17/2013 5:37 PM, Richard Jones
wrote:<br>
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<blockquote cite="mid:51E70E7F.2030406@uconn.edu" type="cite">
<div class="moz-cite-prefix">Hi Dan,<br>
<br>
Welcome back, hope you are doing well.<br>
<br>
Do you have an estimate of the error in the field integral?
We could introduce a bias in the map that zeros out the error
in the field integral to leading order, couldn't we?<br>
<br>
-Richard J.<br>
<br>
<br>
On 7/17/2013 3:26 PM, Daniel Sober wrote:<br>
</div>
<blockquote cite="mid:51E6EFE5.5050701@cua.edu" type="cite"> I'm
back from vacation, and looking harder at the Tosca fields. <br>
My worry about the grid size near the exit edge of a 3 cm gap
is that almost any interpolation procedure is likely to
introduce substantial errors. <br>
The attached plot shows the field vs x at z=0 (magnet
center). <br>
The circles are the Tosca calculated values at x = 32, 33, 34,
..., 44 cm (1 cm steps).<br>
The two curves (with symbols + and ×) show cubic spline
interpolations (using the Numerical Recipes subroutines)
between two different 2 cm grids, corresponding to x = 33, 35,
37, ... cm (odd x) and x = 32, 34, 36, ... cm (even x). For
each integer value of x, one of the two interpolations is
necessarily exact, but the other is far off (~1.5%) near the
field boundary.<br>
The next step is to compare the results of ray-tracing using a
1-cm grid and a 2-cm grid. I will try to set this up using
SNAKE, which I am familiar with (or at least I was 10 years
ago.)<br>
I realize that (1) the errors due to interpolating on a 1-cm
grid will be much smaller than on a 2-cm grid, and (2) the
number of affected points contribute relatively little to the
total field integral, so maybe my worries are for nothing, but
this effect has to be quantified.<br>
Dan<br>
<br>
<br>
<div class="moz-signature">-- <br>
<font color="#ff0000"><i>Daniel Sober,<br>
Professor<br>
Physics Department<br>
The Catholic University of America<br>
Washington, DC 20064<br>
Phone: (202) 319-5856, -5315<br>
E-mail: <a href="mailto:sober@cua.edu">sober@cua.edu</a></i></font><br>
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<br>
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<br>
<div class="moz-signature">-- <br>
<font color="#ff0000"><i>Daniel Sober<br>
Professor<br>
Physics Department<br>
The Catholic University of America<br>
Washington, DC 20064<br>
Phone: (202) 319-5856, -5315<br>
E-mail: <a href="mailto:sober@cua.edu">sober@cua.edu</a></i></font><br>
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